The naming of Hazrat Imam Hussain radiallahu taala anhu and Hazrat Imam Hassan radiallahu taala anhu

When Hazrat Imam Hussain radiallahu taala anhu and Hazrat Imam Hassan radiallahu taala anhu were born on different occasions their father wanted to give them other names, but the Holy Prophet Muhammed Salalaahu Alaihi wasallam specifically named them from these names, these names were specially saved and kept for them .

The names of “al-Hasan” and “al-Husayn” were not known before that; i.e. in the state of ignorance (Jahiliyyah). In fact, their grandfather Prophet Muhammad sallallahualayhi wa sallam was the first one who named with them(who called somebody with these names).
Ibn al-Athir said in “Asad al-Ghabah”

Leaders of the youth of paradise
After they were born the Holy Prophet Muhammed Salalaahu Alaihi wasallam did not give them a basharat that they would be in heaven, but he gave a Basaharat that they would be leaders of the youth of paradise.

The Prophet – blessings and peace be upon him – declared: “these two sons of mine are the leaders of the youth in Paradise.
[Sunan al-Tirmidhi, Kitab al-Manaqib, Manaqib Abi Muhammad al-Hasan, Hadith no. 3793, Vol. 5, Page 426].

Narrated: Ibn Umar
The Messenger of Allah (saw) said: ‘Hasan and Husain will be the leaders of the youth of Paradise, and their father(Syadinna Maula Ali radiallahu taala anhu) is better than them.
Sunan Ibn Majah , Chapter 1 , Book of Sunnah Hadith no: 118